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2 years ago

What is the area of this composite shape?

Mathematics

1 answer:

zlopas [31]2 years ago

7 0

Answer:

Total area = 51 in²

Step-by-step explanation:

Section the shape into a rectangle and a triangle.

Area of a rectangle = width x length

⇒ area = 6 x 7 = 42 in²

Area of a triangle = 1/2 x base x height

⇒ area = 1/2 x (6 - 3) x (13 - 7) = 9 in²

Total area of composite shape = 42 + 9 = 51 in²

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) The density of oil in a circular oil slick on the surface of the ocean at a distance of r meters from the center of the slick

Feliz [49]

Answer:

Therefore the mass of the of the oil is 409.59 kg.

Step-by-step explanation:

Let us consider a circular disk. The inner radius of the disk be r and the outer diameter of the disk be (r+Δr).

The area of the disk

=The area of the outer circle - The area of the inner circle

= $\pi (r+\triangle r)^2- \pi r^2$

$=\pi [r^2+2r\triangle r+(\triangle r)^2-r^2]$

$=\pi [2r\triangle r+(\triangle r)^2]$

Since (Δr)² is very small, So it is ignorable.

∴ $A=2\pi r\triangle r$

The density $\delta (r)= \frac{40}{1+r^2}$

We know,

Mass= Area× density

$=(2r \pi \triangle r)(\frac{40}{1+r^2}})$

Total mass $M=\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i$

Therefore

$\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i=\int_0^5 \frac{80r\pi }{1+r^2}dr$

$=40\pi[ln(1+r^2)]_0^5$

$=40\pi [ln(1+5^2)-ln(1+0^2)]$

$=40\pi ln(26)$

= 409.59 kg (approx)

Therefore the mass of the of the oil is 409.59 kg.

3 0

2 years ago

Instructions: Find mFG.<br> F<br> ?<br> G<br> 55°

Sladkaya [172]

Answer:

110°

Step-by-step explanation:

mFG = 2×<FEG = 2×55 = 110°

Answered by GAUTHMATH

6 0

3 years ago

"If triangle vuw is equiangular, find k and t

balu736 [363]

The answer is b. k=64 t=52.

5 0

3 years ago

What is the value of 4x + 9, when x = 4?

Sonbull [250]

Answer:

The answer would be 25.

4x4=16

16+9=25

Step-by-step explanation:

I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.

4 0

3 years ago

Read 2 more answers

Factorise 4y^2 – 4y + 1

Alona [7]

Answer:

$(2y-1)^{2}$

Step-by-step explanation:

$4y^{2} -4y+1$

Sum = -4

Product = 1

Factors = -1 , -1

$(2y-1)^{2}$

4 0

3 years ago